Question

What is the vertex of `y= x^2-2x+8`?

Answer 1

vertex: `(x,y)=1,7)`

Explanation:

The easiest way to find the vertex is to convert the given equation into "vertex form":
`color(white)("XXX")y=color(green)(m)(x-color(red)(a))^2+color(blue)(b)`
with a vertex at (`color(red)(a),color(blue)(b))`

Given
`color(white)("XXX")y=x^2-2x+8`

Complete the square:
`color(white)("XXX")y=x^2-2x+1 +7`

`color(white)("XXX")y=color(green)(1)(x-color(red)(1))^2+color(blue)(7)`
which is in "vertex-form".

graph{x^2-2x+8 [-3.684, 8.8, 5.06, 11.3]}